Analysis of nonlinear elastic aspects of precursor attenuation in shock-compressed metallic crystals

Abstract

Unsteady characteristics of shock waves in metals, for example elastic precursor decay, have often eluded a complete model description. Historic continuum elastic-plastic theories tend to require excessive initial dislocation densities in order to match experimental observations. Studies incorporating superposition of linear elastodynamic solutions for dislocations, either in analytical solutions or in discrete numerical simulations, omit nonlinear elastic effects and only consider effects of defects immediately at the elastic shock front. Prior analytical treatments of hydrodynamic attenuation consider nonlinearity manifesting as effects of stress gradients or particle velocity gradients immediately behind the front. The present analysis seeks to augment the predictive precursor decay equation from linear elastodynamics to account for elastic nonlinearity and dislocation nucleation in the wake of the precursor shock. A complete solution for the precursor magnitude at a material point is shown to require consideration of the prior history of dislocation generation and the entire flow field behind the elastic shock up to that material point. However, introduction of reasonable simplifying assumptions and basic models for dislocation generation and glide resistance enable derivation of a mathematically tractable relation for precursor decay. This relation is a nonlinear first-order ordinary differential equation that, in non-dimensional form, contains only one scalar parameter controlling the rate of dislocation generation behind the shock. Model predictions that include nonlinear effects are shown to provide a better match to experimental data for three metals. Effects of nonlinearity are shown to emerge early, but not immediately, in the shock attenuation process, and these effects increase in prominence with increasing impact stress.

Instabilities of High Speed Dislocations

“…Since then, continuum models of increasing complexity have been proposed to describe dislocation glide [11][12][13][14][15][16][17][18]. The limiting speeds of dislocations found in continuum models have been attributed to inadequate treatments of the dislocation core [18,19] and the inherent limitations of the small strain approximation [20][21][22].…”

Dislocation drag and its influence on elastic precursor decay

“…Material density dependence is taken into account only indirectly via the limiting velocity within the relativistic factor, or neglected altogether. See [20] for a recent insightful review of high speed dislocation dynamics; for a review of shock compression of crystalline solids and elastic precursor decay, see [21,22] and references therein.…”